Abstract : As its analogue in the continuous framework, the digital fundamental group represents a major information on the topology of discrete objects. However, the fundamental group is an abstract information and cannot directly be encoded in a computer using its deeni-tion. A classical mathematical way to encode a discrete group is to nd a presentation of this group. In this paper, we construct a presentation for the fundamental group of any subset of a digital surface. This presentation can be computed by an eecient algorithm.